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La ecuación:
Ecuación x^2+11=0
Ecuación x^3-x^2-x-1=0
Ecuación 3x-2(3x+4)=10
Ecuación 5x+12=8x+30
Expresar {x} en función de y en la ecuación:
7*x-1*y=0
-11*x-3*y=14
2*x-15*y=-1
-18*x-6*y=-1
Expresiones idénticas
dos *x- uno /x- cinco - tres *x+ dos /x+ cuatro = catorce *x+ once /x^ dos -x- veinte
2 multiplicar por x menos 1 dividir por x menos 5 menos 3 multiplicar por x más 2 dividir por x más 4 es igual a 14 multiplicar por x más 11 dividir por x al cuadrado menos x menos 20
dos multiplicar por x menos uno dividir por x menos cinco menos tres multiplicar por x más dos dividir por x más cuatro es igual a cotangente de angente de orce multiplicar por x más once dividir por x en el grado dos menos x menos veinte
2*x-1/x-5-3*x+2/x+4=14*x+11/x2-x-20
2*x-1/x-5-3*x+2/x+4=14*x+11/x²-x-20
2*x-1/x-5-3*x+2/x+4=14*x+11/x en el grado 2-x-20
2x-1/x-5-3x+2/x+4=14x+11/x^2-x-20
2x-1/x-5-3x+2/x+4=14x+11/x2-x-20
2*x-1 dividir por x-5-3*x+2 dividir por x+4=14*x+11 dividir por x^2-x-20
Expresiones semejantes
2*x-1/x-5+3*x+2/x+4=14*x+11/x^2-x-20
2*x-1/x-5-3*x+2/x+4=14*x+11/x^2+x-20
2*x-1/x-5-3*x+2/x+4=14*x+11/x^2-x+20
(2*x-1)/(x-5)-(3*x+2)/(x+4)=(14*x+11)/(x^2-x-20)
2*x-1/x+5-3*x+2/x+4=14*x+11/x^2-x-20
2*x-1/x-5-3*x+2/x+4=14*x-11/x^2-x-20
2*x-1/x-5-3*x+2/x-4=14*x+11/x^2-x-20
2*x-1/x-5-3*x-2/x+4=14*x+11/x^2-x-20
2*x+1/x-5-3*x+2/x+4=14*x+11/x^2-x-20
2x-1/(x-5)-(3x+2)/x+4=(14x+11)/(x^2-x-20)

2x-1/x-5-3x+2/x+4=14*x+11/x^2-x-20 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

      1             2              11         
2*x - - - 5 - 3*x + - + 4 = 14*x + -- - x - 20
      x             x               2         
                                   x

$$\left(\left(- 3 x + \left(\left(2 x - \frac{1}{x}\right) - 5\right)\right) + \frac{2}{x}\right) + 4 = \left(- x + \left(14 x + \frac{11}{x^{2}}\right)\right) - 20$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

               ______________________                                        /                                                ______________________\
              /             ________                                         |                                               /             ________ |
             /  10525   3*\/ 856353                                          |                                       ___    /  10525   3*\/ 856353  |
          3 /   ----- + ------------                                         |                   ___               \/ 3 *3 /   ----- + ------------ |
     19   \/     1372       392                       403                    |             403*\/ 3                      \/     1372       392      |
x1 = -- + --------------------------- + -------------------------------- + I*|- -------------------------------- + ---------------------------------|
     42                6                          ______________________     |            ______________________                   6                |
                                                 /             ________      |           /             ________                                     |
                                                /  10525   3*\/ 856353       |          /  10525   3*\/ 856353                                      |
                                        1176*3 /   ----- + ------------      |  1176*3 /   ----- + ------------                                     |
                                             \/     1372       392           \       \/     1372       392                                          /

$$x_{1} = \frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)$$

               ______________________                                        /             ______________________                                   \
              /             ________                                         |            /             ________                                    |
             /  10525   3*\/ 856353                                          |    ___    /  10525   3*\/ 856353                                     |
          3 /   ----- + ------------                                         |  \/ 3 *3 /   ----- + ------------                     ___            |
     19   \/     1372       392                       403                    |        \/     1372       392                    403*\/ 3             |
x2 = -- + --------------------------- + -------------------------------- + I*|- --------------------------------- + --------------------------------|
     42                6                          ______________________     |                  6                             ______________________|
                                                 /             ________      |                                               /             ________ |
                                                /  10525   3*\/ 856353       |                                              /  10525   3*\/ 856353  |
                                        1176*3 /   ----- + ------------      |                                      1176*3 /   ----- + ------------ |
                                             \/     1372       392           \                                           \/     1372       392      /

$$x_{2} = \frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right)$$

                                                 ______________________
                                                /             ________ 
                                               /  10525   3*\/ 856353  
                                            3 /   ----- + ------------ 
     19                 403                 \/     1372       392      
x3 = -- - ------------------------------- - ---------------------------
     42            ______________________                3             
                  /             ________                               
                 /  10525   3*\/ 856353                                
          588*3 /   ----- + ------------                               
              \/     1372       392

$$x_{3} = - \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{3} - \frac{403}{588 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{19}{42}$$

x3 = -(3*sqrt(856353)/392 + 10525/1372)^(1/3)/3 - 403/(588*(3*sqrt(856353)/392 + 10525/1372)^(1/3)) + 19/42

Suma y producto de raíces [src]

suma

          ______________________                                        /                                                ______________________\             ______________________                                        /             ______________________                                   \                                               ______________________
         /             ________                                         |                                               /             ________ |            /             ________                                         |            /             ________                                    |                                              /             ________ 
        /  10525   3*\/ 856353                                          |                                       ___    /  10525   3*\/ 856353  |           /  10525   3*\/ 856353                                          |    ___    /  10525   3*\/ 856353                                     |                                             /  10525   3*\/ 856353  
     3 /   ----- + ------------                                         |                   ___               \/ 3 *3 /   ----- + ------------ |        3 /   ----- + ------------                                         |  \/ 3 *3 /   ----- + ------------                     ___            |                                          3 /   ----- + ------------ 
19   \/     1372       392                       403                    |             403*\/ 3                      \/     1372       392      |   19   \/     1372       392                       403                    |        \/     1372       392                    403*\/ 3             |   19                 403                 \/     1372       392      
-- + --------------------------- + -------------------------------- + I*|- -------------------------------- + ---------------------------------| + -- + --------------------------- + -------------------------------- + I*|- --------------------------------- + --------------------------------| + -- - ------------------------------- - ---------------------------
42                6                          ______________________     |            ______________________                   6                |   42                6                          ______________________     |                  6                             ______________________|   42            ______________________                3             
                                            /             ________      |           /             ________                                     |                                               /             ________      |                                               /             ________ |                /             ________                               
                                           /  10525   3*\/ 856353       |          /  10525   3*\/ 856353                                      |                                              /  10525   3*\/ 856353       |                                              /  10525   3*\/ 856353  |               /  10525   3*\/ 856353                                
                                   1176*3 /   ----- + ------------      |  1176*3 /   ----- + ------------                                     |                                      1176*3 /   ----- + ------------      |                                      1176*3 /   ----- + ------------ |        588*3 /   ----- + ------------                               
                                        \/     1372       392           \       \/     1372       392                                          /                                           \/     1372       392           \                                           \/     1372       392      /            \/     1372       392

$$\left(- \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{3} - \frac{403}{588 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{19}{42}\right) + \left(\left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right)\right) + \left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)\right)\right)$$

       /                                                ______________________\     /             ______________________                                   \
       |                                               /             ________ |     |            /             ________                                    |
       |                                       ___    /  10525   3*\/ 856353  |     |    ___    /  10525   3*\/ 856353                                     |
       |                   ___               \/ 3 *3 /   ----- + ------------ |     |  \/ 3 *3 /   ----- + ------------                     ___            |
19     |             403*\/ 3                      \/     1372       392      |     |        \/     1372       392                    403*\/ 3             |
-- + I*|- -------------------------------- + ---------------------------------| + I*|- --------------------------------- + --------------------------------|
14     |            ______________________                   6                |     |                  6                             ______________________|
       |           /             ________                                     |     |                                               /             ________ |
       |          /  10525   3*\/ 856353                                      |     |                                              /  10525   3*\/ 856353  |
       |  1176*3 /   ----- + ------------                                     |     |                                      1176*3 /   ----- + ------------ |
       \       \/     1372       392                                          /     \                                           \/     1372       392      /

$$\frac{19}{14} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right) + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)$$

producto

/          ______________________                                        /                                                ______________________\\ /          ______________________                                        /             ______________________                                   \\ /                                            ______________________\
|         /             ________                                         |                                               /             ________ || |         /             ________                                         |            /             ________                                    || |                                           /             ________ |
|        /  10525   3*\/ 856353                                          |                                       ___    /  10525   3*\/ 856353  || |        /  10525   3*\/ 856353                                          |    ___    /  10525   3*\/ 856353                                     || |                                          /  10525   3*\/ 856353  |
|     3 /   ----- + ------------                                         |                   ___               \/ 3 *3 /   ----- + ------------ || |     3 /   ----- + ------------                                         |  \/ 3 *3 /   ----- + ------------                     ___            || |                                       3 /   ----- + ------------ |
|19   \/     1372       392                       403                    |             403*\/ 3                      \/     1372       392      || |19   \/     1372       392                       403                    |        \/     1372       392                    403*\/ 3             || |19                 403                 \/     1372       392      |
|-- + --------------------------- + -------------------------------- + I*|- -------------------------------- + ---------------------------------||*|-- + --------------------------- + -------------------------------- + I*|- --------------------------------- + --------------------------------||*|-- - ------------------------------- - ---------------------------|
|42                6                          ______________________     |            ______________________                   6                || |42                6                          ______________________     |                  6                             ______________________|| |42            ______________________                3             |
|                                            /             ________      |           /             ________                                     || |                                            /             ________      |                                               /             ________ || |             /             ________                               |
|                                           /  10525   3*\/ 856353       |          /  10525   3*\/ 856353                                      || |                                           /  10525   3*\/ 856353       |                                              /  10525   3*\/ 856353  || |            /  10525   3*\/ 856353                                |
|                                   1176*3 /   ----- + ------------      |  1176*3 /   ----- + ------------                                     || |                                   1176*3 /   ----- + ------------      |                                      1176*3 /   ----- + ------------ || |     588*3 /   ----- + ------------                               |
\                                        \/     1372       392           \       \/     1372       392                                          // \                                        \/     1372       392           \                                           \/     1372       392      // \         \/     1372       392                                    /

$$\left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6}\right)\right) \left(\frac{403}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{19}{42} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{6} + \frac{403 \sqrt{3}}{1176 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}}{3} - \frac{403}{588 \sqrt[3]{\frac{3 \sqrt{856353}}{392} + \frac{10525}{1372}}} + \frac{19}{42}\right)$$

-11 
----
 14

$$- \frac{11}{14}$$

-11/14

Respuesta numérica [src]

x1 = 1.00087393302137 + 0.466003755108876*i

x2 = 1.00087393302137 - 0.466003755108876*i

x3 = -0.644605008899888

x3 = -0.644605008899888

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Expresiones idénticas

Expresiones semejantes

2*x-1/x-5-3*x+2/x+4=14*x+11/x^2-x-20 la ecuación

Solución numérica:

Solución

2x-1/x-5-3x+2/x+4=14*x+11/x^2-x-20 la ecuación